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In this work we show that tensor-network architectures have especially prospective properties for privacy-preserving machine learning, which is important in tasks such as the processing of medical records. First, we describe a new privacy vulnerability that is present in feedforward neural networks, illustrating it in synthetic and real-world datasets. Then, we develop well-defined conditions to guarantee robustness to such vulnerability, which involve the characterization of models equivalent under gauge symmetry. We rigorously prove that such conditions are satisfied by tensor-network architectures. In doing so, we define a novel canonical form for matrix product states, which has a high degree of regularity and fixes the residual gauge that is left in the canonical forms based on singular value decompositions. We supplement the analytical findings with practical examples where matrix product states are trained on datasets of medical records, which show large reductions on the probability of an attacker extracting information about the training dataset from the model&amp;apos;s parameters. Given the growing expertise in training tensor-network architectures, these results imply that one may not have to be forced to make a choice between accuracy in prediction and ensuring the privacy of the information processed.<\/jats:p>","DOI":"10.22331\/q-2024-07-25-1425","type":"journal-article","created":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T16:24:20Z","timestamp":1721924660000},"page":"1425","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":6,"title":["Privacy-preserving machine learning with tensor networks"],"prefix":"10.22331","volume":"8","author":[{"given":"Alejandro","family":"Pozas-Kerstjens","sequence":"first","affiliation":[{"name":"Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland"},{"name":"Constructor Institute, 8200 Schaffhausen, Switzerland"},{"name":"Instituto de Ciencias Matem\u00e1ticas (CSIC-UAM-UC3M-UCM), 28049 Madrid, Spain"},{"name":"Departamento de An\u00e1lisis Matem\u00e1tico, Universidad Complutense de Madrid, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Senaida","family":"Hern\u00e1ndez-Santana","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada a la Ingenier\u00eda Industrial, Universidad Polit\u00e9cnica de Madrid, 28006 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 Ram\u00f3n","family":"Pareja Monturiol","sequence":"additional","affiliation":[{"name":"Instituto de Ciencias Matem\u00e1ticas (CSIC-UAM-UC3M-UCM), 28049 Madrid, Spain"},{"name":"Departamento de An\u00e1lisis Matem\u00e1tico, Universidad Complutense de Madrid, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Castrill\u00f3n L\u00f3pez","sequence":"additional","affiliation":[{"name":"Departamento de \u00c1lgebra, Geometr\u00eda y Topolog\u00eda, Universidad Complutense de Madrid, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giannicola","family":"Scarpa","sequence":"additional","affiliation":[{"name":"Escuela T\u00e9cnica Superior de Ingenier\u00eda de Sistemas Inform\u00e1ticos, Universidad Polit\u00e9cnica de Madrid, 28031 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carlos E.","family":"Gonz\u00e1lez-Guill\u00e9n","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada a la Ingenier\u00eda Industrial, Universidad Polit\u00e9cnica de Madrid, 28006 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"P\u00e9rez-Garc\u00eda","sequence":"additional","affiliation":[{"name":"Instituto de Ciencias Matem\u00e1ticas (CSIC-UAM-UC3M-UCM), 28049 Madrid, Spain"},{"name":"Departamento de An\u00e1lisis Matem\u00e1tico, Universidad Complutense de Madrid, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2024,7,25]]},"reference":[{"key":"0","unstructured":"Apple. ``Differential privacy overview&apos;&apos;. https:\/\/www.apple.com\/privacy\/docs\/Differential_Privacy_Overview.pdf (2021). 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